Brooks-type theorems for choosability with separation

@article{Kratochvl1998BrookstypeTF,
  title={Brooks-type theorems for choosability with separation},
  author={Jan Kratochv{\'i}l and Zsolt Tuza and Margit Voigt},
  journal={Journal of Graph Theory},
  year={1998},
  volume={27},
  pages={43-49}
}
We consider the following type of problems. Given a graph G = (V; E) and lists L(v) of allowed colors for its vertices v 2 V such that jL(v)j = p for all v 2 V and jL(u) \ L(v)j c for all uv 2 E, is it possible to nd a \list coloring", i.e., a color f (v) 2 L(v) for each v 2 V , so that f (u) 6 = f (v) for all uv 2 E ? We prove that every graph of maximum degree admits a list coloring for every such list assignment, provided p p 5:437c. Apart from a multiplicative constant, the result is tight… CONTINUE READING

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